ASDANISOTROPIC
SPACE DYNAMICS
中文AI Researcher
ASDBoundary temperature and first law
EQUATION REGISTRY

Boundary temperature and first law

Fixed G₀, c and σ_h with E=Mc²; the temperature coefficient adopts the Bekenstein–Hawking reference normalization. The last line assumes differentiable E(S,J,Q), not an already solved rotating strong-field microstate.

Theory · EFFECTIVE MODELEquation version 1.0.0

Based on the final manuscript · Chapter 2

ASD-WEB-GRV-051
Tbdy=c632πkBσhG02M,dEbdy=Tbdy dSbdy,σh=c34G0ℏ ⟹ Tbdy=ℏc38πG0kBM,Cbdy=−Mc2Tbdy,dEbdy=Tbdy dS+ωbdy dJ+Vbdy dQ.\begin{aligned}T_{\rm bdy}&=\frac{c^6}{32\pi k_B\sigma_hG_0^2M},\qquad dE_{\rm bdy}=T_{\rm bdy}\,dS_{\rm bdy},\\\sigma_h=\frac{c^3}{4G_0\hbar}&\ \Longrightarrow\ T_{\rm bdy}=\frac{\hbar c^3}{8\pi G_0k_BM},\qquad C_{\rm bdy}=-\frac{Mc^2}{T_{\rm bdy}},\\dE_{\rm bdy}&=T_{\rm bdy}\,dS+\omega_{\rm bdy}\,dJ+\mathcal V_{\rm bdy}\,dQ.\end{aligned}

Fixed G₀, c and σ_h with E=Mc²; the temperature coefficient adopts the Bekenstein–Hawking reference normalization. The last line assumes differentiable E(S,J,Q), not an already solved rotating strong-field microstate.
Chapter reference: Final collected manuscript · Chapter 2 §V.8 (2.88)—(2.94) · ASD-BOOK-ddbade997b45

Assumptions and derivation Registry and dependencies Research this equation Discuss this equation

Source and ID

ASD-WEB-GRV-051 is the stable website equation ID. It retains existing links and does not replace the manuscript reference. Use the copy button to obtain LaTeX.

Return to premises and derivation
Adopted source, conditions and previous versions

Final collected manuscript · Chapter 2 §V.8 (2.88)—(2.94)

Fixed G₀, c and σ_h with E=Mc²; the temperature coefficient adopts the Bekenstein–Hawking reference normalization. The last line assumes differentiable E(S,J,Q), not an already solved rotating strong-field microstate.

Conditions retained in this adoption

  • Fixed G₀; isolated, static, spherically symmetric, uncharged exterior.
  • Areal radius, actual spatial length and reference optical path are defined separately.
  • Weak-field perturbation, slow-rotation far field and boundary statistics each have separate conditions.

Specific unresolved source issues

  • Microscopic source matching, dynamical strong fields and full boundary-state dynamics remain open.

Source locators: p0784 · p0786 · p0794 · p0796 · p0802 · p0807 · p0820 · p0822 · p0831 · p0840 · p0849 · p0856 · p0876 · p0878 · p0886 · p0891 · p0899 · p0937 · 最终合订稿 · 第二章 §五.8 (2.88)—(2.94)

Manuscript SHA-256: ddbade997b45913248e588953b1d27ccb9c7c206c3c8d992d3aef2364a64836e

Download source identity manifest

The manifest identifies the source; it is not the complete manuscript. Adopting this source does not upgrade evidence or grant a new licence.

Previous source, retained as history

·

DEPENDS ON

Dependencies

inputBoundary energy balance and area entropyASD-WEB-GRV-050
USED BY

Uses of this equation

DocumentStrong-field closureDocumentCompact Objects · Static Optics and Strong-field Boundaries
Discuss this page Browse all equations